Scattering matrix invariants of Floquet topological insulators

Abstract

Similar to static systems, periodically driven systems can host a variety of topologically non-trivial phases. Unlike the case of static Hamiltonians, the topological indices of bulk Floquet bands may fail to describe the presence and robustness of edge states, prompting the search for new invariants. We develop a unified description of topological phases and their invariants in driven systems, by using scattering theory. We show that scattering matrix invariants correctly describe the topological phase, even when all bulk Floquet bands are trivial. Additionally, we use scattering theory to introduce and analyze new periodically driven phases, such as weak topological Floquet insulators, for which invariants were previously unknown. We highlight some of their similarities with static systems, including robustness to disorder, as well as some of the features unique to driven systems, showing that the weak phase may be destroyed by breaking translational symmetry not in space, but in time.

11 pages, 8 figures. New title and references, expanded discussion. Accepted for publication in PRB

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Cited by in corpus (55)

• Experimental observation of anomalous topological edge modes in a slowly-driven photonic lattice
• The anomalous Floquet-Anderson insulator as a non-adiabatic quantized charge pump
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Non-Hermitian Floquet topological phases with arbitrarily many real-quasienergy edge states
• Exceptional Points in a Non-Hermitian Topological Pump
• Aperiodic Weak Topological Superconductors
• Complex classes of periodically driven topological lattice systems
• Measuring Topological Invariants in Disordered Discrete Time Quantum Walks
• Floquet topological phases in a spin-1/2 double kicked rotor
• Recipe for creating an arbitrary number of Floquet chiral edge states
• Bulk-Edge correspondence for two-dimensional Floquet topological insulators
• Non-Hermitian Pseudo-Gaps
• Tuning anomalous Floquet topological bands with ultracold atoms
• Detecting topological invariants in chiral symmetric insulators via losses
• Floquet Weyl Phases in a Three Dimensional Network Model
• Non-Hermitian Floquet topological phases in the double-kicked rotor
• Driving protocol for a Floquet topological phase without static counterpart
• Floquet engineering to exotic topological phases in systems of cold atoms
• Band flatness optimization through complex analysis
• Time-induced second-order topological superconductors
• A computational study of two-terminal transport of Floquet quantum Hall insulators
• Line nodes and surface Majorana flat bands in static and kicked p-wave superconducting Harper model
• Topology and localization of a periodically driven Kitaev model
• Mixed higher-order topology: boundary non-Hermitian skin effect induced by a Floquet bulk
• Strongly Disordered Floquet Topological Systems
• Chiral 1D Floquet topological insulators beyond rotating wave approximation
• Topological invariants for Floquet-Bloch systems with chiral, time-reversal, or particle-hole symmetry
• Localization counteracts decoherence in noisy Floquet topological chains
• Topological edge states in two-gap unitary systems: A transfer matrix approach
• Counter-propagating edge states in Floquet topological insulating phases
• Universal driving protocol for symmetry-protected Floquet topological phases
• Electronic transport in one-dimensional Floquet topological insulators via topological and nontopological edge states
• Effective vacua for Floquet topological phases: A numerical perspective on switch-function formalism
• Anomalous Floquet topological crystalline insulators
• Unconventional Floquet topological phases from quantum engineering of band inversion surfaces
• Dynamical characterization of Weyl nodes in Floquet Weyl semimetal phases
• Efficient computation of the $W_3$ topological invariant and application to Floquet-Bloch systems
• Floquet topological phase transitions in a kicked Haldane-Chern insulator
• Network model for higher-order topological phases
• Simulating Floquet topological phases in static systems
• Transport signatures of symmetry protection in 1D Floquet topological insulators
• Three dimensional two-band Floquet topological insulator with $Z_2$ index
• Anomalous levitation and annihilation in Floquet topological insulators
• Photo-induced SU(3) topological material of spinless fermions
• Floquet-Weyl and Floquet-topological-insulator phases in a stacked two-dimensional ring-network lattice
• Anatomy of a periodically driven p-wave superconductor
• Topological reflection matrix
• Topological delocalization in the completely disordered two-dimensional quantum walk
• Quantum phase transitions and a disorder-based filter in a Floquet system
• Relation between scattering matrix topological invariants and conductance in Floquet Majorana systems
• Dynamical Chiral Symmetry and Symmetry-Class Conversion in Floquet Topological Insulators
• Proposal for realizing anomalous Floquet insulators via Chern band annihilation
• Floquet engineering of spin-valley selective transport in jacutingaite
• Topology and quantum phases of low dimensional fermionic systems
• Noise resilience of two-dimensional Floquet topological phases